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Continuous dependence and uniqueness theorems in boundary-initial value problems for a class of porous bodies occupying bounded or unbounded domains

Part of: Flows in porous media; filtration; seepage

Published online by Cambridge University Press:  26 February 2010

Alessandra Borrelli  and
Maria Cristina Patria
Alessandra Borrelli
Affiliation:
Istituto Matematico dell'Università, via Machiavelli 35, 44100, Ferrara, Italy.
Maria Cristina Patria
Affiliation:
Istituto Matematico dell'Università, via Machiavelli 35, 44100, Ferrara, Italy.
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Summary

In this paper the authors formulate a boundary-initial value problem for a linear elastic porous body saturated with an inviscid fluid and establish a continuous dependence theorem (Theorem 2) and two uniqueness theorems (Theorems 3, 4) for a particular class of such continua. Theorems 2, 3 are proved without hypotheses on the sign of the constants and, if the domain is unbounded, under mild assumptions on the spatial asymptotic behaviour of the field variables. Theorem 4 holds for body-forces not equal to zero and, if the domain is unbounded, without restrictions upon the behaviour of the unknown fields at infinity, but under suitable conditions on the sign of the constants.

MSC classification

Secondary: 76S05: Flows in porous media; filtration; seepage
Type
Research Article
Information
Mathematika , Volume 31 , Issue 2 , December 1984 , pp. 196 - 213
Copyright
Copyright © University College London 1984

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